Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1711.10494

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening

Nathan W. C. Leigh·Aaron M. Geller·B. McKernan·K. E. S. Ford·M. -M. Mac Low·J. Bellovary·Z. Haiman·W. Lyra·J. Samsing·M. O'Dowd·B. Kocsis·S. Endlich
View original source ↗Read source document ↗Export metadata ↓

Abstract

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disk components hosting a super-massive black hole (SMBH). We determine the total number of encounters $N_{\rm GW}$ needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for $N_{\rm GW}$ to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically $N_{\rm GW} \lesssim$ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disk. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because disks enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.

Explore related subjects

astro-ph.GAastro-ph.HE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nathan W. C. Leigh, Aaron M. Geller, B. McKernan, K. E. S. Ford, M. -M. Mac Low, J. Bellovary, Z. Haiman, W. Lyra, J. Samsing, M. O'Dowd, B. Kocsis, S. Endlich. 2017-11-28. On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening. https://doi.org/10.1093/mnras%2Fstx3134

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-lensing binaries in globular clusters -- predictions for ELT

Self-lensing (SL) represents a powerful technique for detecting compact objects in binary systems through gravitational microlensing effects, when a compact companion transits in front of its luminous partner. We present the first comprehensive study of SL probability within globular cluster (GC) environments, utilizing synthetic stellar populations from MOCCA simulations to predict detection rates for the Extremely Large Telescope (ELT). Our analysis incorporates finite-size lens effects for white dwarf (WD) lenses and the specific observational characteristics of the ELT/MICADO instrument. We find that present-day GCs contain 1-50 SL sources with magnifications $μ_\mathrm{sl} > 1+10^{-8}$, strongly dependent on initial binary fraction, with systems dominated by WD lenses paired with low-mass main-sequence companions. The predicted populations exhibit characteristic bimodal magnitude distributions with peaks at $m \approx 24$ and 32 mag at 10 kpc distance, and typical Einstein ring crossing times of $τ_\mathrm{eff} \sim 2$ hours. ELT observations should achieve detection efficiency of 0.015-10 sources in $\sim150$ nearby GC after a year of observations depending on distance and survey strategy, with nearby clusters ($D \lesssim 10$ kpc) offering the highest yields. Multi-year monitoring campaigns with daily cadence provide order-of-magnitude improvements over single observations through enhanced photometric precision and increased detection probability. Our results demonstrate that coordinated ELT surveys of Galactic GCs represent a viable approach for probing hidden binary populations and compact object demographics in dense stellar environments, with comprehensive programs potentially yielding up to 10-100 well-characterized SL sources after first 5 years of observations suitable for statistical studies of binary evolution in extreme environments.

astro-ph.GA↗
arXiv2026

Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations

The correlation between black hole mass, $M_{\rm bh}$, and stellar velocity dispersion, $σ_0$, is revisited using 137 galaxies with quantitative bar strengths and enhanced morphological awareness. Interpreted within the `Triangal' evolutionary framework, gas-rich and gas-poor assembly pathways emerge in the $M_{\rm bh}$-$σ_0$ diagram. To quantify these scaling relations, a symmetric Bayesian hierarchical regression code, dubbed the Symmetric COvariance Population Estimator (SCOPE), is introduced. Unlike conditional estimators (e.g., LINMIX), SCOPE derives the intrinsic population covariance, natively accommodating asymmetric measurement errors while guaranteeing directional invariance between axes. Primeval, dust-poor S0 galaxies (including dwarf early-type galaxies with $R_{\rm e,gal}$ ~ 1 kpc) follow a shallow relation ($M_{\rm bh}\proptoσ_0^{2.5\text{--}3.1}$). Explained via the virial theorem, this flattening reframes expectations for intermediate-mass black holes. In contrast, tracing the `Disc Down-sizing' sequence - where dry mergers erase discs - yields a steep relation for massive elliptical and ellicular galaxies ($M_{\rm bh}\proptoσ_0^{7.8\pm1.4}$). Applying a single, monolithic scaling relation across all morphologies inadvertently averages over different formation histories, potentially skewing AGN virial $f$-factor calibrations and systematically under-predicting the ultra-massive black holes needed to generate the nanohertz gravitational wave background. Furthermore, strongly barred, dust-poor S0 galaxies appear offset to higher $σ_0$, while this dynamical signature is lost in the complexities of spiral galaxies. Ultimately, these morphology-dependent relations provide physically-motivated benchmarks for cosmological simulations and a framework for disentangling regimes driven by AGN feedback from those driven by mergers.

astro-ph.GA↗
arXiv2026

Profile Analysis of the Multiwavelength 2.1-year Oscillations of PG 1553+113

We investigate the morphology of the oscillation profiles of the blazar PG~1553+113 in relation to its well-known $\sim$2.1 yr periodicity. We identify individual cycles in the $γ$-ray, X-ray, UV, and optical light curves and characterize their temporal profiles using analytical models for single- and multi-peaked events. We find that the oscillations are generally described by a broad activity envelope with shorter-timescale substructure, showing that the $\sim$2.1 yr signal is not a strictly sinusoidal or self-similar modulation. The internal morphology varies across cycles and energy bands. This is particularly evident in X-rays, where all analyzed cycles show a strong formal preference for multi-component profiles, unlike the $γ$-ray band, where several cycles admit statistically comparable empirical descriptions. The contemporaneous MWL oscillations show broadly aligned activity episodes, but the timing and relative amplitudes of secondary components are not systematically repeated. This suggests that a common long-term modulation affects the broadband emission, while additional local or energy-dependent processes shape individual cycles. Such a picture is compatible with a geometric, jet-related contribution to the broad recurrent envelope, with intrinsic variability superimposed on it. We also identify new cycles with a dominant peak accompanied by weaker twin-peak-like features, similar to structures previously discussed in a supermassive black hole binary scenario for PG~1553+113. Although our results do not provide definitive evidence for this interpretation, the recurrence of comparable morphologies in newly analyzed cycles keeps this scenario viable.

astro-ph.GA↗